The way to do the math is to list them year mo day and subtract
Herbert died 1887 10 14 borrow a mo18870944 Subtract20 08 20200820
so born 1867 01 24 or 1/24/1867.
but that's relying on someone remembering his birth date correctly and properly subtracting from the death date...
I usually use the earliest date in the census, because it's the freshest and easiest to remember - so I would use age 6 in 1870, which gives birth year as 1864, which would put his birth before Henry died.
Since the DNA remains virtually constant over many generations - any male BARTLETT (over 21) from your line would do.
My earlier question was wheather John was previously married (before he marrid Almira)?
Anyway, good luck, and let me know when someone wants to do DNA.You can learn a lot about it at www.familytreedna.com